The file does not need Basic/Windows authentication, as long as the header is sent.
This works fine on the Deskop, but online (Power BI Premium) I get the following error (and a 400 error). I think it's attempting to connect and authenticate, without the header in the "Scheduled" configuration screen. The header is sent as a HTTP header, unfortunately, so I suspect it's not sent when configuring the data source credentials.
Failed to update data source credentials: The credentials provided for the Web source are invalid
On Power BI Premium, whilst connecting to a gateway
Unable to connect: We encountered an error while trying to connect to . Details: "We could not register this data source for any gateway instances within this cluster. Please find more details below about specific errors for each gateway instance.
So it's the same issue.
I cannot get the source to authenticate without the header, and the "Edit Credentials" screen doesn't send the header when testing the connectivity.
The Web API credentials don't work, as it doesn't send the API Key and Value as a HTTP header.